Question: Simplify the following expression: $ q = \dfrac{7}{8} - \dfrac{k + 2}{-7k - 5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7k - 5}{-7k - 5}$ $ \dfrac{7}{8} \times \dfrac{-7k - 5}{-7k - 5} = \dfrac{-49k - 35}{-56k - 40} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{k + 2}{-7k - 5} \times \dfrac{8}{8} = \dfrac{8k + 16}{-56k - 40} $ Therefore $ q = \dfrac{-49k - 35}{-56k - 40} - \dfrac{8k + 16}{-56k - 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-49k - 35 - (8k + 16) }{-56k - 40} $ Distribute the negative sign: $q = \dfrac{-49k - 35 - 8k - 16}{-56k - 40}$ $q = \dfrac{-57k - 51}{-56k - 40}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{57k + 51}{56k + 40}$